{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6d948c51",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "682fe83b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(xold):\n",
    "    return 3-7/(xold+3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b4006e6b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "第 1 次 误差为 0.25  目前new为 1.25\n",
      "第 2 次 误差为 0.10294117647058831  目前new为 1.3529411764705883\n",
      "第 3 次 误差为 0.038950715421303794  目前new为 1.391891891891892\n",
      "第 4 次 误差为 0.014261954261954202  目前new为 1.4061538461538463\n",
      "第 5 次 误差为 0.005159003008164964  目前new为 1.4113128491620113\n",
      "第 6 次 误差为 0.0018579597662775615  目前new为 1.4131708089282888\n",
      "第 7 次 误差为 0.0006680604310627114  目前new为 1.4138388693593515\n",
      "第 8 次 误差为 0.00024007480110488366  目前new为 1.4140789441604564\n",
      "第 9 次 误差为 8.625574822418436e-05  目前new为 1.4141651999086806\n",
      "第 10 次 误差为 3.098827548275729e-05  目前new为 1.4141961881841634\n",
      "第 11 次 误差为 1.1132564863070016e-05  目前new为 1.4142073207490264\n",
      "第 12 次 误差为 3.999345426608514e-06  目前new为 1.414211320094453\n",
      "第 13 次 误差为 1.436749680561178e-06  目前new为 1.4142127568441336\n",
      "第 14 次 误差为 5.161462395264493e-07  目前new为 1.4142132729903731\n",
      "第 15 次 误差为 1.8542326940540477e-07  目前new为 1.4142134584136425\n",
      "第 16 次 误差为 6.661248419526089e-08  目前new为 1.4142135250261267\n",
      "循环次数为 16 终值为 1.4142135250261267\n"
     ]
    }
   ],
   "source": [
    "xold=1\n",
    "new=1\n",
    "i=0\n",
    "listNew=[]\n",
    "listI=[]\n",
    "listD=[]\n",
    "while True:\n",
    "    xnew=func(xold)\n",
    "    listNew.append(xnew)\n",
    "    d=abs(xnew-xold)\n",
    "    xold=xnew\n",
    "    i=i+1\n",
    "    listI.append(i)\n",
    "    listD.append(d)\n",
    "    print('第',i,'次 误差为',d,' 目前new为',xnew)\n",
    "    if d<0.0000001:\n",
    "        break\n",
    "print('循环次数为',i,'终值为',xold)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "83abbc78",
   "metadata": {},
   "outputs": [],
   "source": [
    "y1=[1.414]*len(listI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "680e8db9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dd38b8b80>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(listI,listNew)\n",
    "plt.plot(listI,y1)\n",
    "plt.xlabel(\"i\",fontsize=18)\n",
    "plt.ylabel(\"xnew\",fontsize=18)\n",
    "plt.legend([\"i_xnew\",\"y=1.414\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "599a753b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "第 1 次 误差为 97.06796116504854  目前new为 2.9320388349514563\n",
      "第 2 次 误差为 1.112071568175679  目前new为 1.8199672667757774\n",
      "第 3 次 误差为 0.2722592871492917  目前new为 1.5477079796264857\n",
      "第 4 次 误差为 0.08694489443272779  目前new为 1.4607630851937579\n",
      "第 5 次 误差为 0.030001322309403333  目前new为 1.4307617628843545\n",
      "第 6 次 误差为 0.01062553679286471  目前new为 1.4201362260914898\n",
      "第 7 次 误差为 0.0037978242748013535  目前new为 1.4163384018166885\n",
      "第 8 次 误差为 0.0013618676635327454  目前new为 1.4149765341531557\n",
      "第 9 次 误差为 0.0004889249551789376  目前new为 1.4144876091979768\n",
      "第 10 次 误差为 0.00017560284301021412  目前new为 1.4143120063549666\n",
      "第 11 次 误差为 6.307921130388472e-05  目前new为 1.4142489271436627\n",
      "第 12 次 误差为 2.266023703056952e-05  目前new为 1.4142262669066321\n",
      "第 13 次 误差为 8.140499941688972e-06  目前new为 1.4142181264066904\n",
      "第 14 次 误差为 2.924426677708425e-06  目前new为 1.4142152019800127\n",
      "第 15 次 误差为 1.0505856999909469e-06  目前new为 1.4142141513943127\n",
      "第 16 次 误差为 3.7741801350854587e-07  目前new为 1.4142137739762992\n",
      "第 17 次 误差为 1.355857051077436e-07  目前new为 1.414213638390594\n",
      "第 18 次 误差为 4.8708553856968706e-08  目前new为 1.4142135896820403\n",
      "循环次数为 18 终值为 1.4142135896820403\n"
     ]
    }
   ],
   "source": [
    "xold=100\n",
    "new=1\n",
    "i=0\n",
    "listNew=[]\n",
    "listI=[]\n",
    "listD=[]\n",
    "while True:\n",
    "    xnew=func(xold)\n",
    "    listNew.append(xnew)\n",
    "    d=abs(xnew-xold)\n",
    "    xold=xnew\n",
    "    i=i+1\n",
    "    listI.append(i)\n",
    "    listD.append(d)\n",
    "    print('第',i,'次 误差为',d,' 目前new为',xnew)\n",
    "    if d<0.0000001:\n",
    "        break\n",
    "print('循环次数为',i,'终值为',xold)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3421a87e",
   "metadata": {},
   "outputs": [],
   "source": [
    "y1=[1.414]*len(listI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3ab2fc68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dd393fdf0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(listI,listNew)\n",
    "plt.plot(listI,y1)\n",
    "plt.xlabel(\"i\",fontsize=18)\n",
    "plt.ylabel(\"xnew\",fontsize=18)\n",
    "plt.legend([\"i_xnew\",\"y=1.414\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f1426a02",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
